The expression for sum & product of roots of quadratic equation is gotten from the general expression of quadratic equation. If the distinct roots are α and β, then

α + β = -b/a (sum of roots)

αβ =c/a (product of roots)

Example 1 – find the sum and products of 2x^{2} + 3x – 1 = 0

Solution

2x^{2} + 3x – 1 = 0

a =2, b = 3, c = -1

Let α and β be the roots of the equation, then

α+β= -b/a= -3/2

αβ = c/a = -1/2

Example 2 – find the sum and products of 3x^{2} – 5x -2 = 0

Solution

3x^{2} -5x -2 =0

a= 3, b= -5, c= -2

let α and β be the roots of the equation, then

α+β= -b/a = 5/3

αβ= c/a= -2/3

**NB: **The quadratic equation whose root are α and β is

** (X**** – α )(X**** – β) = 0**

**X**^{2}** – (α +β)X**** + αβ = 0**

Example – Find the quadratic equation whose roots are 3 & -2

Solution

α=3 and β=-2

α+β = 3 + (-2) = 1

αβ = 3 x -2 = -6

X^{2} – (α +β)x + αβ = 0

X^{2 }– (1)X + (-6) = 0

X^{2} – X -6 = 0

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